2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics


Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 1 No. 4
The Three-wave Method and Its Applications
M. A. Abdou, E. M. Abulwafa
Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
E-mail: m_abdou_eg@yahoo.com
Abstract: Travelling waves may be composed of different frequencies and velocities. This paper proposes a multi-wave method for finding exact multi-solitary solutions. Two models of special interest in physics are chosen, namely, the (2+1)-dimensional KdV equation and the (2+1)-dimensional Ito equation to illustrate the effectiveness of the suggested method and some new wave solutions with three different velocities and frequencies are obtained. As a result, a new periodic type of three wave solutions including periodic solitary solutions, doubly periodic solitary solution and breather type of two solitary solutions are obtained using Hirota's bilinear form and the extended three wave-method. The extended three-soliton method is reliable and effective and can also be applied to solve other types of higher dimensional integrable and non-integrable systems.

Keywords: Extended Three-wave solution; periodic cross-kink wave; breather cross-kink wave; Bilinear form; Painleve's analysis

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